Pricing and Hedging of SOFR Derivatives under Differential Funding Costs and Collateralization

Since the 1970s, the LIBOR has served as a fundamental measure for floating term rates across multiple currencies and maturities. Loans and many derivative securities, including swaps, caps and swaptions, still rely on LIBOR as the reference forward-looking term rate. However, in 2017 the Financial Conduct Authority announced the discontinuation of LIBOR from the end of 2021 and the New York Fed declared the backward-looking SOFR as a candidate for a new reference rate for interest rate swaps denominated in U.S. dollars. We first outline the classical single-curve modelling framework before transitioning to the multi-curve framework where we examine arbitrage-free pricing and hedging of SOFR-linked swaps without and with collateral backing. As hedging instruments, we take liquidly traded SOFR futures and either common or idiosyncratic funding rates for the hedge and margin account. For concreteness, a one-factor model based on Vasicek's equation is used to specify the joint dynamics of several overnight interest rates, including the SOFR, EFFR, and unsecured funding rate, although multi-factor term structure models could also be employed